The most common and most likely answer to this crossword clue is the 8 letter word RECUSANT
I've seen this crossword clue in The Daily Telegraph
R
E
C
U
S
A
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T
Buddy explains!

The straight part
We know that "Dissenter" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case dissenter = recusant.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does RECUSANT mean?
RECUSANT noun- Someone refusing to attend Church of England services, between the sixteenth and early nineteenth centuries.
- Anyone refusing to submit to authority or regulation.
- Pertaining to a recusant or to recusancy